Nanofluidic channels with gradual depth change for reducing entropic barrier of biopolymers

ABSTRACT

A device for passing a biopolymer molecule includes a nanochannel formed between a surface relief structure, a patterned layer forming sidewalls of the nanochannel and a sealing layer formed over the patterned layer to encapsulate the nanochannel. The surface relief structure includes a three-dimensionally rounded surface that reduces a channel dimension of the nanochannel at a portion of nanochannel and gradually increases the dimension along the nanochannel toward an opening position, which is configured to receive a biopolymer.

BACKGROUND Technical Field

The present invention relates to nanodevices, and more particularly todevices and methods for stretching biopolymers using nanofluidicchannels.

Description of the Related Art

Accurate and inexpensive sensing of biopolymers, especially nucleicacids (DNA, RNA), is important for many scientific and biomedicalapplications. A high-throughput and robust device to electricallysequence the biopolymers is of great importance. Solid-state bio-sensingtechniques, such as artificial nanopores and channels, have beenintegrated into fluidics for sensing (sequencing) many types ofbiopolymer molecules, including DNA, RNA, proteins, etc. For precisesingle molecule sensing of biopolymers, a linearized or fully stretchedbiopolymer chain conformation is desirable. However, thermodynamicallyfavored conformation of flexible biopolymers, such as a single strainDNA, includes a coiled conformation. One key issue for sensingbiopolymers is a large entropic energy barrier for biopolymers (e.g.,low entropy for stretched biopolymers and high entropy for coiled ones)to be transported from a large dimension into a smaller dimension. Sucha large energy barrier originates from the entropic difference of theflexible polymer.

A large energy barrier greatly lowers the translocation rate of thebiopolymers, and can cause very long clogging events in nano-scalechannels. Such a large entropy change can cause configurationalinstabilities of the biopolymers and even drive them to randomly coiland decoil inside the nanofluidic channels or pores. All of these andother problems can lead to reduced and clogged events and thus severelyaffect proper detection of molecules. Moreover, the entropic energybarrier height increases with the biopolymer chain length, making itvery undesirable for precise and high-speed sensing of long biopolymers.

SUMMARY

A device for passing a biopolymer molecule includes a nanochannel formedbetween a surface relief structure, a patterned layer forming sidewallsof the nanochannel and a sealing layer formed over the patterned layerto encapsulate the nanochannel. The surface relief structure includes athree-dimensionally rounded surface that reduces a channel dimension ofthe nanochannel at a portion of nanochannel and gradually increases thedimension along the nanochannel toward an opening position, which isconfigured to receive a biopolymer.

Another device for passing a biopolymer molecule includes a substrate,and a surface relief structure formed on the substrate and having atleast one three-dimensionally rounded surface providing a graduallychanging depth from a position on the surface relief structure along achannel. The surface relief structure forms a first surface of thechannel. A patterned layer is formed on the surface relief structure andforms sidewalls of the channel. A sealing layer is formed over thepatterned layer to form a second surface of the channel opposite thefirst surface.

A method for fabricating a device for evaluating biopolymer moleculesincludes patterning a surface relief material on a substrate; annealingthe surface relief material to reflow the surface relief material toform a surface relief structure that includes a rounded surface;planarizing a channel dielectric layer formed over the surface reliefmaterial; patterning the channel dielectric layer to shape a nanochannelover the surface relief material; and forming a sealing layer over thechannel dielectric layer to encapsulate a channel, wherein the channelincludes a channel dimension at a portion of nanochannel and graduallyincreases the dimension along the nanochannel toward an openingposition, which is configured to receive a biopolymer.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1A is a cross-sectional view of a fluidic channel device withgradually changing depth for reduction of entropic barrier in accordancewith the present principles;

FIG. 1B is a top-view of the channel of FIG. 1A.

FIG. 2 shows the fluidic channel device of FIG. 1 along with an electricfield distribution graph along the channel, an entropy (S) graph of DNAalong the channel and graphs of electrostatic energy (U) and Gibbs freeenergy (G=U−T*S) of DNA in accordance with the present principles;

FIG. 3 is a cross-sectional view of a fluidic channel device withgradually changing depth showing controlling of the nano-fluidic channeldepth by tuning parameters such as a contact angle of a surface reliefon the substrate, radius of the curvature of the reflowed surface reliefmaterial, a size of the reflowed material cap, and a height of thereflowed material cap in accordance with the present principles;

FIG. 4 shows linear plots and log plots of radius of the curvature R,height h, and a size of the reflowed material cap r as a function ofcontact angle with given volumes in accordance with the presentprinciples;

FIG. 5 shows graphs of channel depth versus x position for controllingnanochannel depths by volume and contact angle (5-90°) for volumes V₁and V₂, and contact angles along the x-axis from 0 to 20 μm; and alongthe x-axis from 0 to 5 μm in accordance with the present principles;

FIG. 6A is a cross-sectional view and a top view of a substrate having adielectric or surface layer formed thereon to control contact angle inaccordance with the present principles;

FIG. 6B is a cross-sectional view and a top view of the device of FIG.6A showing surface relief materials patterned on the surface layer orsubstrate in accordance with the present principles;

FIG. 6C is a cross-sectional view and a top view of the device of FIG.6B showing an anneal to reflow surface relief materials in accordancewith the present principles;

FIG. 6D is a cross-sectional view and a top view of the device of FIG.6C showing a deposition of a thin dielectric coating in accordance withthe present principles;

FIG. 6E is a cross-sectional view and a top view of the device of FIG.6D showing a deposition of a thick insulating dielectric material inaccordance with the present principles;

FIG. 6F is a cross-sectional view and a top view of the device of FIG.6E showing a chemical mechanical polish (CMP) planarization and reactiveion etch (RIE) to reduce a thickness of insulating channel dielectriclayer in accordance with the present principles;

FIG. 6G is a cross-sectional view and a top view of the device of FIG.6F showing patterning of a nano-fluidic channel in accordance with thepresent principles;

FIG. 6H is a cross-sectional view and a top view of the device of FIG.6G showing sealing of nano-fluidic channels in accordance with thepresent principles;

FIG. 7 is a cross-sectional view and a top view of devices showing localheating of surface relief materials before and after heating inaccordance with the present principles;

FIG. 8A is a top view showing different shapes, surface densities andlocations of surface relief material structures in accordance with thepresent principles;

FIG. 8B is a top view showing a transverse bar shape rounded inaccordance with the present principles;

FIG. 9A is a cross-sectional view showing integration of electrodes onnanochannels of surface relief materials including single top-bottomelectrodes, where the bottom electrode can be the surface reliefmaterial in accordance with the present principles;

FIG. 9B is a cross-sectional view showing integration of electrodes onnanochannels of surface relief materials including multiple top-bottomelectrodes, where the bottom electrode can be the surface reliefmaterial in accordance with the present principles; and

FIG. 9C is a cross-sectional view showing integration of electrodes onnanochannels of surface relief materials including molecular sensingelectrodes, where the bottom electrode can be the surface reliefmaterial in accordance with the present principles.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In accordance with the present principles, a nanodevice includes ananochannel having a patterned and reflowed surface relief material toform micro- or nano-scale caps. Such caps can be controlled to havegradual changes in thickness, and serve as a scaffold to define achannel bottom surface, hence yielding a gradually changing channeldepth. A flexibly tuned and gradually changing channel depth permitsminimized entropic barrier for molecules to translocate. Electrodes canbe integrated into the channels for controlling the molecular motion ormolecular sensing.

A method for fabricating nanofluidic channels with gradually changingdepth are provided by building such channels on a surface reliefmaterial with a tunable curvature. The curvature of the surface reliefmaterial can be designed by engineering its volume, shape, and contactangle on an underlying substrate. Using this, the channel depth andhence confinement of biopolymers can be accurately and flexiblyoptimized. This can minimize the entopic barrier of the biopolymer toenter into a narrowest channel region and yield a higher translocationrate.

It is to be understood that the present invention will be described interms of a given illustrative architecture having a wafer, substrate orother solid-state material; however, other architectures, structures,substrate materials and process features and steps may be varied withinthe scope of the present invention.

It will also be understood that when an element such as a layer, regionor substrate is referred to as being “on” or “over” another element, itcan be directly on the other element or intervening elements may also bepresent. In contrast, when an element is referred to as being “directlyon” or “directly over” another element, there are no interveningelements present. It will also be understood that when an element isreferred to as being “connected” or “coupled” to another element, it canbe directly connected or coupled to the other element or interveningelements may be present. In contrast, when an element is referred to asbeing “directly connected” or “directly coupled” to another element,there are no intervening elements present.

A design for an integrated circuit chip or nanodevice may be created ina graphical computer programming language, and stored in a computerstorage medium (such as a disk, tape, physical hard drive, or virtualhard drive such as in a storage access network). If the designer doesnot fabricate chips or the photolithographic masks used to fabricatechips, the designer may transmit the resulting design by physical means(e.g., by providing a copy of the storage medium storing the design) orelectronically (e.g., through the Internet) to such entities, directlyor indirectly. The stored design is then converted into the appropriateformat (e.g., GDSII) for the fabrication of photolithographic masks,which typically include multiple copies of the chip design in questionthat are to be formed on a wafer. The photolithographic masks areutilized to define areas of the wafer (and/or the layers thereon) to beetched or otherwise processed.

Methods as described herein may be used in the fabrication of integratedcircuit chips or nanodevices. The resulting integrated circuit chips canbe distributed by the fabricator in raw wafer form (that is, as a singlewafer that has multiple unpackaged chips), as a bare die, or in apackaged form. In the latter case the chip is mounted in a single chippackage (such as a plastic carrier, with leads that are affixed to amotherboard or other higher level carrier) or in a multichip package(such as a ceramic carrier that has either or both surfaceinterconnections or buried interconnections). In any case the chip isthen integrated with other chips, discrete circuit elements, and/orother signal processing devices as part of either (a) an intermediateproduct, such as a motherboard, or (b) an end product. The end productcan be any product that includes integrated circuit chips, ranging fromtoys and other low-end applications to advanced computer products havinga display, a keyboard or other input device, and a central processor.

Reference in the specification to “one embodiment” or “an embodiment” ofthe present principles, as well as other variations thereof, means thata particular feature, structure, characteristic, and so forth describedin connection with the embodiment is included in at least one embodimentof the present principles. Thus, the appearances of the phrase “in oneembodiment” or “in an embodiment”, as well any other variations,appearing in various places throughout the specification are notnecessarily all referring to the same embodiment.

It is to be appreciated that the use of any of the following “/”,“and/or”, and “at least one of”, for example, in the cases of “A/B”, “Aand/or B” and “at least one of A and B”, is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of both options (A andB). As a further example, in the cases of “A, B, and/or C” and “at leastone of A, B, and C”, such phrasing is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of the third listedoption (C) only, or the selection of the first and the second listedoptions (A and B) only, or the selection of the first and third listedoptions (A and C) only, or the selection of the second and third listedoptions (B and C) only, or the selection of all three options (A and Band C). This may be extended, as readily apparent by one of ordinaryskill in this and related arts, for as many items listed.

Referring now to the drawings in which like numerals represent the sameor similar elements and initially to FIGS. 1A and 1B, a nanodevice ornanofluidic structure 100 includes a fluidic channel 121 with graduallychanging depth for the reduction of entropic barrier in accordance withone illustrative embodiment. FIG. 1A shows a cross-sectional view andFIG. 1B shows a top view of the nanofluidic structure 100. Thenanofluidic structure 100 includes a substrate material 101 coated witha surface coating layer 102. The substrate material 101 may include,e.g., an insulator, a semiconductor, conductor or another suitable rigidmaterial. The surface coating layer 102 may include self-assembledmonolayer (SAM, e.g., a single layer of organic molecules), dielectric,metal, glass, semiconductor, etc. A surface relief material or cap 110may be formed in place or shaped by reflow. Surface relief material orstructure 110 may be formed in a spherical cap shape or any other shapehaving a gradual changing profile. Surface relief material 110 mayinclude a glass, a resist, a polymer, such as polycarbonate,polyethylene, poly (methyl methacrylate) (PMMA), a metal (e.g., asolder), etc.

An optional dielectric layer 111 may be employed to coat the surfacerelief cap 110. The dielectric layer 111 may be employed to control adimension of the nanofluidic channel 121 and is formed in an insulatingmaterial on top of the coated spherical cap 110. A dielectric material122 seals the nanofluidic channel 121. A biopolymer 131, e.g., a DNAmolecule, is illustratively shown to demonstrate operation of thenanofluidic structure 100. The nanofluidic channel 121 may include alarger feed port 107 and/or exit port 107 in communication with thenanofluidic channel 121.

Referring to FIG. 2, the nanofluidic structure 100 with a graduallychanging nano-fluidic channel depth for reduction of an entropic barrieris depicted in cross-section. A graph 202 shows electric fielddistribution along the channel. A graph 204 shows entropy (S) of DNAalong the channel. A graph 206 shows electrostatic energy (U) and theGibbs free energy (G=U−T*S) of DNA, where T represents the thermodynamictemperature in an absolute scale, e.g., Kelvin. In the graph 206, qV isindicated where q is charge and V is voltage.

The spherical cap has a gradually changed height and thus yields agradually changing channel depth, with the smallest depth at a zenith ofthe spherical cap. The electrical field reaches a peak value at theshallowest channel depth region (graph 202). As a biopolymer enters froma deep channel region and moves into a shallowest region of the channel(at the zenith), it stretches as the channel depth reduces with itsentropy value (S) gradually decreasing (graph 204). This yields a smoothchanging Gibbs free energy (G=U−TS) slope (graph 206), where U is theelectrostatic energy of the charged biopolymer and T is the temperature.Therefore, the smoothly transitioned channel depth leads to a minimizedentropic energy barrier for the biopolymers to transport through thechannel, which is important for the translocation and stretching ofbiopolymers.

Referring to FIG. 3, in one embodiment, the surface relief material 110is completely melted to an ideal spherical cap. Nano-fluidic channeldepth is controlled by tuning the contact angle of a surface relief onthe substrate. R is the radius of the curvature of the reflowed surfacerelief material, θ is the contact angle, r is the size of the reflowedmaterial cap, h is the height of the reflowed material cap, do is theminimal channel depth, d is the variable channel depth along the xdirection, D is the maximum channel depth. In this case, therelationships between the radius of curvature R, the cap height h, thecap size r and the contact angle θ may include the following:(R−h)²+r²=R², r=R*sin(θ); h₀=R−R*cos(θ).

Assuming the volume of the surface relief material V is conserved, thevolume of the spherical cap V can be written as:V=π/6*h*(3r ² +h ²)=π/3*h ²*(3R−h)=π/3*R ³*(2−3*cos(θ)+cos(θ)³)=V ₀

From above, it is clear R can be derived from the initial volume V₀ withthe contact angle θ given. Then, h and r can be calculated from R and θ.Assuming the nanochannel is sealed with a flat film (122 in FIG. 1A),the smallest depth is d₀, and the channel depth d or d(x) along the xdirection can be calculated as d(x)=d₀+(R−sqrt(R²−x²)). This geometry isillustrative as other geometries are also contemplated and with thescope of the present principles.

Referring to FIG. 4, where the surface relief material 110 is completelymelted to an ideal spherical cap, the parameters R, r, and h are allcalculated at different contact angles. Two samples of initial volumesfor the surface relief material 110 were used, V₁=10² μm³ (e.g., 1*10*10μm³ or 10¹¹ nm³) and V₂=10⁴ μm³ (e.g., 1*100*100 μm³ or 10¹³ nm³). Infact, the 100 times difference in volume causes a 4.64 (=(V₂/V₁)^(1/3))times difference in the two sets of curves of R, r, and h.

Examples for determining geometrical parameters R, h, and r by volumeand contact angle include a first graph 302, which is a linear plotshowing R 304, h 306, and r 308 as a function of contact angle (θ) withgiven volumes (V₁=1×10¹¹, solid lines, and V₂=1×10¹³ nm³, dashed lines),and a second graph 310, which plots of R 312, h 314, and r 316 as afunction of contact angle (θ) with given volumes (V₁=1×10¹¹, solidlines, and V₂=1×10¹³ nm³, dashed lines). r is related to channel depth.

Referring to FIG. 5, examples for controlling nanochannel depths byvolume and contact angle are illustratively shown. A graph 402 showschannel depths with different contact angles (5-90°) for a cap 420(surface relief material 110) with a volume V₁=1×10¹¹ nm³ along thex-axis from 0 to 20 μm (indicated by line 424) from a center position ofthe cap 420. A graph 404 shows channel depths with different contactangles (5-90°) for the cap 420 with a volume V₁=1×10¹¹ nm³ along x-axisfrom 0 to 5 μm (indicated by line 426). A graph 406 shows channel depthswith different contact angles (5-90°) for a cap 422 with a volumeV₂=1×10¹³ nm³ along the x-axis from 0 to 20 μm (indicated by line 424)from a center position of the cap 422. A graph 408 shows channel depthswith different contact angles (5-90°) for the cap 422 with a volumeV₂=1×10¹³ nm³ along x-axis from 0 to 5 μm (indicated by line 426).

A nanochannel depth (d) can be determined assuming two volumes of thesurface relief material (110) for caps 420 and 422 as 10¹¹ nm³ (graphs402, 404) and 10¹³ nm³ (graphs 406, 408). The channel depth d increasesvery smoothly with a small contact angle θ, but increases quitedramatically for large contact angles. An initial volume of the surfacerelief material (110) for caps 420, 422 also has an impact on thenanochannel depth slope. At a large distance away from the cap centerwhere x=0, for example x=15 μm, the channel depth is larger for a largercap. This is because the depth is fixed as the maximum channel depthD=h+d₀ for a small cap, and the channel depth increases as a function ofx because of a greater r and h for a larger cap. At a small distanceaway from the cap center where x=0, for example x=2 μm, the channeldepth is larger for a small cap. This is because the cap height changesmore abruptly over a same distance x.

This shows that the cap geometry and the channel depth can flexibly bedesigned by tuning the contact angle and the surface relief material(110). In practical embodiments, the channel depth may need to changefrom <5 nm to 100-500 nm over a distance of 1-100 μm. The contact angleand the volume of the surface relief material can be determinedaccording to the corresponding h and r dimensions.

Referring to FIGS. 6A-6H, a fabrication scheme is illustratively shownto achieve such a channel-on-cap configuration for a nanodevice 100. Anexample of fabricating nanochannels on a reflowed surface reliefmaterial includes depositing a surface layer to control contact angle,patterning surface relief materials and annealing to reflow surfacerelief materials. A thin dielectric coating is deposited and a thickinsulating dielectric material is formed on top. A chemical mechanicalplanarization (CMP) and reactive ion etch (RIE) are employed to reducethe thickness of insulating channel dielectric layer. Nano-fluidicchannels are patterned, and sealed. Each of FIGS. 6A-6H include across-section view (CS), a top view (TV), and a set of axes X, Y and Zfor each view.

Referring to FIG. 6A, a dielectric layer 102 is deposited on top of asubstrate material 101. The dielectric layer 102 is employed as aninsulating coating of a nanochannel bottom surface, and is also employedas a layer to flexibly tune the contact angle of surface reliefmaterial. The dielectric layer 102 can be either organic or inorganic,it can be realized by physical deposition, chemical deposition, chemicalassembly, etc., and the material of dielectric layer 102 may include,e.g., SiO₂, Al₂O₃, Si₃N₄, organic monolayer, etc. The material ofsubstrate 101 can be any material, either organic or inorganic, and itcan be, e.g., Si, SiO₂, Si₃N₄, metal, plastic, etc. The dielectric layer(surface layer) 102 controls the surface tension, which in turndetermines the contact angle and the shape of reflowed materials.

Referring to FIG. 6B, a surface relief material 110 is patterned by acombination of micro-nano fabrication techniques, which may includelithography, deposition, etching, etc. An initial volume of the surfacerelief material 110 is determined in this process. The shape of thesurface relief material 110 does not have to be square or rectangular.

Referring to FIG. 6C, an annealing process is performed to fully orpartially melt the surface relief material 110 to form a cap. Theannealing method can be light illumination (e.g., ultraviolet (UV),excimer, visible, infrared (IR), etc.), heat, etc. Preferably, theheating temperature exceeds the melting or glass-transition temperatureof the material to fully reflow the material, which makes the materialround, preferably in three dimensions. The temperature could also beslightly lower than the melting or glass-transition temperature to onlysoften the surface relief material. The surface relief material does nothave to be round. A localized heat is also possible to partially meltthe surface relief pattern. In an alternate embodiment, the surfacerelief material 110 is formed separately and adhered to the dielectriclayer 102.

Referring to FIG. 6D, the annealed surface relief cap (110) isoptionally coated with another dielectric layer 111. The coating ordielectric layer material may include, e.g., Al₂O₃, SiO₂, etc. Thedeposition can be by atomic layer deposition (ALD), plasma enhancedchemical vapor deposition (PECVD), low pressure CVD (LPCVD),evaporation, etc. The coating material or dielectric layer 111 can beused to harden the underlying surface-relief cap (110), protect the cap(110) from etching that follows, and act as an etch-stop layer tocontrol channel depth.

Referring to FIG. 6E, an insulating dielectric layer 120 is coated ontop of the spherical cap 110 or dielectric layer 111, if employed. Layer120 is to be used to form a fluidic channel. The insulating dielectriclayer 120 (channel material) may include, e.g., SiO₂, Si₃N₄, etc.

Referring to FIG. 6F, the insulating dielectric layer 120 is planarizedby polishing (e.g., CMP) and optionally thinned by etching, e.g.,reactive ion etching or wet chemical etching. The minimum dielectriclayer height is set to do, which may be, e.g., less than 100 nm andpreferably less than 20 nm.

Referring to FIG. 6G, a nano-channel 121 is patterned and aligned on topof the spherical cap (110) region by a series of micro-nano fabricationtechniques, which may include lithography, deposition, etching, etc. Thenanochannels 121 may have different widths at different regions, e.g.,with the smallest dimensions on top of the center of the spherical cap110. The nano-channel 121 may be configured with tapers 107 or otherfeatures to assist in loading and translocating biopolymers.

Referring to FIG. 6H, the channels 121 are sealed with a dielectricmaterial 122. The sealing method may include wafer bonding and/orpitching off small venting holes using a sacrificial channel material.

Referring to FIG. 7, in another embodiment, the cap may be formed usingdifferent heating techniques to result in different shapes. Localheating of surface relief materials is shown during heating (610) andafter heating (612). A localized heat source 602, e.g., a laser orfocused light, can be employed to locally modify a shape of surfacerelief materials 110. This can result in arbitrary and asymmetricchannel depth profiles.

Referring to FIG. 8A, in other embodiments, structure geometry,dimension, and patterning density of the surface relief patterns (110)can be flexibly changed, according to the need for different dimensionsand densities for different channel applications. Tuning shapes, surfacedensity, and locations of surface relief material structures may includecomplex compound surfaces and shapes. Structures other than thosedepicted in FIG. 8A are also contemplated.

Referring to FIG. 8B, in one practical embodiment, surface reliefmaterial 110 can be patterned as a very long (e.g., 1-10 μm length) baralong the Y direction (shown under the insulating dielectric layer 120).In this way, the melted surface relief material is less spherical butrather cylindrical with a uniform round cap along the Y direction. Thenanochannel 121 can be very easily aligned to the surface reliefmaterials 110 (if the top cap is very spherical then the laterallithography alignment to pattern the nanochannels on top of the capwould be very stringent).

Referring to FIGS. 9A-9C, the nanodevices in accordance with the presentprinciples may be configured in a plurality of ways, e.g., by includingelectrodes or other structures for driving or controlling biopolymers orother molecules. Integrating electrodes with nanochannels on surfacerelief materials may include single top-bottom electrodes, where thebottom electrodes can be the surface relief material itself, may beembedded in or on the surface relief material, may include multiple topand bottom electrodes, may include molecular sensing electrodes, etc.

Referring to FIGS. 9A and 9B, the surface relief structures 110 can beintegrated with electrodes for better control of biopolymers and/orsensing the biopolymers. The surface relief material itself can beemployed as an electrode. This may include coating the surface reliefmaterial 110 with a conductive material, placing a conductor in thesurface relief material 110, making the surface relief material 110 froma conductive material, or provide electrical conductors coated with alayer of linker molecules.

A top electrode 115 and/or 116 may be deposited and patterned orotherwise adhered to the dielectric layer 122. A method for controllinga biopolymer 131 passing between the electrode 115 and the surfacerelief material 110 can be based on electrostatic interaction of thecharged biopolymer with applied electrical potential. There can bemultiple electrodes 116 (FIG. 9B) or a single (FIG. 9A) top electrode.In one embodiment, the surfaces of electrodes 115 and 116 can befunctioned (lined or coated) with organic molecules or linker moleculeswhich can interact with the biopolymer, for example, to hold thebiopolymer, sense the biopolymer or otherwise interact with thebiopolymer being stretched or sensed. The linker molecules may includewith self-assembled molecules with a functional head-group, such as,e.g., benzamide and/or imidazole. Other linker molecules may be employedas well.

Referring to FIG. 9C, in another embodiment, a sensing circuit 135 maybe connected between an electrode 117 and the surface relief material110 to form an ohmic contact using fluid in the channel 121. Electricalcurrent signals can be used to detect and even sequence the biopolymer131 as it moves through the channel 121. Other configurations are alsocontemplated.

It should be understood that the biopolymers may employ electrophoresisto drive or translocate biopolymers 131. The motion of dispersedparticles, under the influence of a spatially uniform electric field, isemployed to move, relative to a fluid disposed in the channel 121, thebiopolymer through the nanochannel 121.

It should also be noted that, in some alternative implementations, thefunctions noted in the figures may occur out of the order noted in thefigures. For example, two steps shown in succession may, in fact, beexecuted substantially concurrently, or the steps may sometimes beexecuted in the reverse order, depending upon the functionalityinvolved.

Having described preferred embodiments for nanofluidic channels withgradual depth change for reducing entropic barrier of biopolymers (whichare intended to be illustrative and not limiting), it is noted thatmodifications and variations can be made by persons skilled in the artin light of the above teachings. It is therefore to be understood thatchanges may be made in the particular embodiments disclosed which arewithin the scope of the invention as outlined by the appended claims.Having thus described aspects of the invention, with the details andparticularity required by the patent laws, what is claimed and desiredprotected by Letters Patent is set forth in the appended claims.

What is claimed is:
 1. A method for fabricating a microfluidic channel,comprising: patterning a surface relief material on a substrate, whereinthe surface relief material has an initial volume, V₀; partially orcompletely melting the surface relief material to form a cap having arounded surface determined by a contact angle, θ, and the initialvolume, V₀, of the melted surface relief material; and forming ananochannel over the rounded surface of the cap in a channel material,wherein the rounded surface of the cap forms a bottom surface of thenanochannel.
 2. The method as recited in claim 1, wherein the surfacerelief material is completely melted.
 3. The method as recited in claim2, wherein a radius of curvature of the cap is determined byR=[3/π*(V₀/(2−3*cos (θ)+cos(θ)³))]^(1/3), where θ is the contact angle,V₀ is the initial volume, R is the radius of curvature of the cap. 4.The method as recited in claim 3, further comprising, forming a surfacecoating layer between the substrate and the surface relief material tocontrol the contact angle of the completely melted surface reliefmaterial.
 5. The method as recited in claim 1, wherein the channelmaterial in which the nanochannel is formed is an insulating dielectriclayer formed over the cap, and wherein the nanochannel is aligned withthe top-center of the rounded surface of the cap.
 6. The method asrecited in claim 5, further comprising, polishing the insulatingdielectric layer to reduce the thickness of the insulating dielectriclayer over the cap; and forming a top dielectric layer over the channeldielectric layer to seal the nanochannel.
 7. The method as recited inclaim 5, wherein the cap has the initial volume, V₀, of 1×10¹³ nm³. 8.The method as recited in claim 5, wherein the nanochannel in theinsulating dielectric layer has a minimum depth at the top-center of therounded surface of the cap and an increasing channel depth in adirection away from the top-center formed by the rounded surface.
 9. Themethod as recited in claim 5, further comprising forming a dielectriccoating on the cap before forming the insulating dielectric layer overthe cap, wherein the dielectric coating is a different material than theinsulating dielectric layer, so the dielectric coating acts as an etchstop layer.
 10. The method as recited in claim 5, wherein the contactangle is between 5° and 90°.
 11. The method as recited in claim 5,further comprising forming electrodes adjacent to the nanochannel forcontrolling and/or sensing a biopolymer.
 12. A method for fabricating amicrofluidic channel, comprising: depositing a surface coating layer onthe substrate to control the surface tension of the substrate;patterning a surface relief material on the surface coating layer;completely melting the surface relief material to form a cap having arounded surface determined by a contact angle, θ, and an initial volume,V₀, of the melted surface relief material; forming an insulatingdielectric layer over the cap; and forming a nanochannel over therounded surface of the cap in the insulating dielectric layer, whereinthe rounded surface of the cap forms a bottom surface of thenanochannel.
 13. The method as recited in claim 12, wherein a radius ofcurvature of the cap is determined by R=[3/π*(V₀/(2−3*cos(θ)+cos(θ)³))]^(1/3), where θ is the contact angle, V₀ is the initialvolume, R is the radius of curvature of the cap.
 14. The method asrecited in claim 12, further comprising, polishing the insulatingdielectric layer to reduce the thickness of the insulating dielectriclayer over the cap, wherein the bottom surface of the nanochannel has agradually changing height determined by a radius of curvature of thespherical cap.
 15. The method as recited in claim 14, further comprisingforming a top dielectric layer over the insulating dielectric layer toseal the nanochannel, wherein the gradually changing height of thebottom surface provides a gradually changing channel depth between thebottom surface and top dielectric layer.
 16. A method for fabricating amicrofluidic channel, comprising: partially or completely melting apatterned surface relief material on a substrate to form a cap having arounded surface determined by a contact angle, θ, and an initial volume,V₀, of the melted surface relief material; forming an insulatingdielectric layer over the cap; and forming a nanochannel in theinsulating dielectric layer, wherein the rounded surface of the capforms a bottom surface of the nanochannel.
 17. The method as recited inclaim 16, wherein the bottom surface of the nanochannel has a graduallychanging height determined by the radius of curvature of the cap. 18.The method as recited in claim 17, further comprising forming a topdielectric layer over the insulating dielectric layer to seal thenanochannel, wherein the gradually changing height of the bottom surfaceprovides a gradually changing channel depth between the bottom surfaceand top dielectric layer.
 19. The method as recited in claim 17, whereinthe cap has the initial volume, V₀, of 1×10¹¹ nm³.
 20. The method asrecited in claim 17, wherein the nanochannel has a varying width withthe smallest width at the top-center of the cap.